Aircraft: MD-11
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical

Event occurred at cruise; non-radar environment; HF position reports with ATC. Both I (right seat) and the Relief Pilot (left seat) were at the controls when both yokes started to vibrate to the degree of a light buzz. I was the pilot not flying and autopilot number 1 was engaged. I immediately checked altitude; airspeed and VSI. All parameter were normal. Aircraft was holding altitude; airspeed and had a zero VSI. Next we checked all circuit breakers to include autopilot and stall warning systems; and I did a quick test of the warning lights. All circuit breakers were in. The dull continuous vibration remained making it difficult to hold the yoke for any length of time. We tried swamping to autopilot number 2; this did not alleviate the situation. I consulted the QRH and Aircraft Operating Manual (AOM) for any reference to flight control malfunction or inappropriate stall warning or stall warning system malfunction. There was not applicable reference in the QRH or AOM for our situation. At this point the Captain relieved the Relief Pilot from the left seat and informed me that I should take my rest and that he and the Relief Pilot would work the situation. I let the Relief Pilot into the right seat and headed into crew rest. Before I retired I briefed the Captain that we checked all our lights and circuit breakers and found no anomalies. We consulted the AOM and QRH and found no reference for our situation. Upon returning to the cockpit after my two and a half hours of rest; the vibration has ceased in both yokes. Vibration much less than normal stick shaker activation as experienced in the simulator. No other stall warning indications were illuminated. Our airspeed was around 300 KIAS and the V min foot was about 250 KIAS. The PLI was about 5 degrees above actual aircraft pitch attitude. We called Dispatch via satellite phone to inform them of this issue. Dispatch connected us to Maintenance Control. We described the situation to Maintenance Control and queried as to what the problem may be. We told Maintenance we alternated and disconnected the autopilot however the mild shaking continued. We did our best to work together as a team; however the information Maintenance provided did not help clear the discrepancy. In an effort to provide advance notice to the Company; we asked Maintenance Control to inform our destination Maintenance of the problem. After our discussion with Maintenance Control; we terminated the satellite phone call. After discussing this situation further with the crew; I decided to check the security of the stick shaker cannon plug on the Captain's yoke. Much to my surprise; the cannon plug was loosely secured and became disconnected from the yoke; as that happened; a Level 1 alert 'Stall Warn Fail' illuminated. The mild shaking remained. I re-secured the cannon plug and the alert extinguished. When we checked the security of the First Officer's stick shaker cannon plug; it too was loosely secured and disconnected. The mild yoke shaking ceased and no alert message illuminated. I did not re-secure the cannon plug and left it disconnected for Maintenance to re-secure. The remainder of the flight was uneventful. While airborne and in cruise flight; I did a complete and thorough logbook write-up. I also discussed and debriefed Maintenance after block in. A MD11's control columns were mildly vibrating at cruise with no other indications. Both stall warning cannon plugs were found loose and when the left was connected; with the right disconnected; the vibration ceased.